1. Field of the Invention
The present invention generally relates to method, system and computer program product used in computer aided engineering analysis, more particularly to enabling adaptive discretization refinement for general three-dimensional (3-D) shell structures in mesh-free analysis.
2. Description of the Related Art
Finite element analysis (FEA) is a computerized method widely used in industry to model and solve engineering problems relating to complex systems since its invention in late 1950's. With the advent of the modern digital computer, FEA has been implemented as FEA computer program product. Basically, the FEA computer program product is provided with a model of the geometric description and the associated material properties at each point within the model. In this model, the geometry of the system under analysis is represented by solids, shells and beams of various sizes, which are called elements. The vertices of the elements are referred to as nodes. The individual elements are connected together by a topological map, which is usually called mesh. The model is comprised of a finite number of elements, which are assigned a material name to associate with material properties. The model thus represents the physical space occupied by the object under analysis along with its immediate surroundings. The FEA computer program product then refers to a table in which the properties (e.g., stress-strain constitutive equation, Young's modulus, Poisson's ratio, thermo-conductivity) of each material type are tabulated. Additionally, the conditions at the boundary of the object (i.e., loadings, physical constraints, etc.) are specified. In this fashion a model of the object and its environment is created.
FEA computer program product can be classified into two general types, implicit analysis computer program product and explicit analysis computer program product. The implicit analysis computer program product uses an implicit equation solver to solve a system of coupled linear equations. Such computer program product is generally used to simulate static or quasi-static problems. Explicit computer program product does not solve coupled equations but explicitly solves for each unknown assuming them uncoupled. The explicit analysis computer program product usually uses central difference time integration which requires very small solution cycles or time steps for the method to be stable and accurate. The explicit analysis computer program product is generally used to simulate short duration events where dynamics are important such as impact type events.
Although FEA has been successfully applied to many fields to simulate various engineering problems, there are some instances that FEA may not be advantageous due to numerical compatibility condition is not the same as the physical compatibility condition of a continuum. For example, in Lagrangian type of computations, one may experience mesh distortion, which can either end the computation altogether or result in dramatic deterioration of accuracy. In addition, the FEA often requires a very fine mesh in problems with high gradients or a distinct local character, which can be computationally expensive. For this reason, adaptive re-meshing in FEA has been developed. In the adaptive re-meshing process, only the high strain gradient portion of the structure requires mesh refinement. Hence, the simulation can be carried out with computational efficiency.
However, the FEA adaptive re-meshing procedures for simulations of impact/penetration problems, explosion/fragmentation problems, flow pass obstacles, and fluid-structure interaction problems etc., have become formidable tasks to undertake. The difficulties for employing adaptive mesh in FEA are not only re-meshing, but also mapping the state variables from the old mesh to the new mesh. In FEA, a linear adaptivity is used in the adaptive re-meshing process, which means that each of the newly adapted mesh is constraint to the original mesh surfaces. As a result of this restriction, the analytical results are often too stiff in deformation. It is evident that this process often introduces numerical errors; frequent re-mesh is not desirable. Therefore, it would be desirable to have the new improved techniques to numerically analyze a general 3-D shell structure with adaptive discretization.